Typically, the mining of a resource may take place over a period of 15-30 years before the mine is exhausted to a position where further mining is not economic.
The process of mine development and design and long-term scheduling is based on spatial interpretation of drillhole data. Thus, drillholes are drilled over the region to be mined and data relating to the grade of the resource is obtained. The drillholes are generally drilled a reasonable distance apart because this procedure is relatively expensive. A block model of the region to be mined is created and typically, the block model may contain between 50,000 to 1,000,000 blocks which are to be scheduled for mining over the period of 15-30 years. A block is that material enclosed by a rectangular prism in the ground and may contain air to a volumetric percentage strictly less than 100%. A block model is a collection of non-intersecting blocks that are usually, but not necessarily, spatially connected and which contain no less than all material considered to have economic value in a mining enterprise. The objective of the scheduling procedure is to find the block extraction sequence which produces the maximum possible net present value (NPV) and obeys a number of constraints. The constraints include:    (a) geotechnical slope constraints which are modelled by a set of precedence rules constraining the order of extraction of individual blocks;    (b) mining constraints, i.e. total maximum amount of rock which can be mined in one time period (usually 1 year);    (c) processing constraints, i.e. maximum amount or ore which can be processed through a given processing plant in one time period;    (d) and the market constraints, i.e. the maximum amount of metal, which can be sold in one time period;    (e) Any other constraints salient to the practical mining operation including but not restricted to maximum limits in sinking-rate and available ore.
A schedule is a period of extraction for each block and a destination for each block (waste, stockpile or process plant.
The ore body model which is built up from the drillhole data is a deterministic model created by spatial interpretation of the data using some kind of so-called Kriging procedure. This enables each of the blocks in the model to be assigned a resource grade (i.e. the amount of the resource present in the block). The resource grade information is then used to determine the scheduling of the mining operation, and also whether a particular block is sent for processing to extract the resource, sent to waste, or stockpiled for later processing.
Because the drillholes are generally drilled some distance apart, the drillhole data is usually sparse and therefore this introduces inherent errors in the deterministic block model. To some extent, this can be overcome by providing more data by drilling more holes. However, as is explained above, the drilling of the drillholes is expensive and therefore, this is not desirable.
Thus, traditionally open pit mine planning is based on the block model which is built up using some kind of interpolation technique such as the Kriging procedure so that a single model is produced. This single model is assumed to be a fair representation of reality and is used for mine design and optimisation. The design process consists of three main steps:    (a) finding the block extraction sequence which produces the best net present value whilst satisfying geotechnical slope constraints;    (b) designing the practically mineable mine phases (so-called push backs) which are roughly based on the optimal block sequence; and    (c) optimising the mining schedule and cut-off grades.
The cut-off grade (COG) is defined as the threshold such that the blocks with a grade above it are sent to the processing plant and with a grade below it are treated as waste. It can be constant for the whole life of mine, or can be variable, i.e. dependent on the period of extraction.
In practice, the open mine is divided into a number of the mining phases, which are mined bench by bench, each bench being represented by a horizontal layer of blocks within the given mining phase and having the same elevation. A bench within a mining phase is sometimes referred to as a “panel” (one or more layers of blocks). The mining phases can be mined one by one from top to bottom. However, this kind of schedule is usually sub-optimal. Mining several phases simultaneously and applying a variable cut-off grade can produce much better results. There are several commercially available packages which claim to optimise the schedule and cut-off grade using a single block model representation of the resource. However, it is difficult to estimate their effectiveness as the upper theoretical limit on the net present value remains unknown.
The standard optimisation technique widely used in many industrial applications is the linear and integer programming (e.g. Padberg, 2003). However, in order for this program to operate satisfactorily, the problem to be solved needs to be formulated as a linear one.